Hello all,
First, I would like to commend Sheepdog for posting such an intriguing question and on keeping the overall tone of this thread civil.
I pronounce 'Arch mage' as 'Arch' + 'Mage'! I pronounce 'Arch mage' as such because the word seems to be made up of two words with the 'Arch' part (to me) being a prefixed designation or title that does not need a hyphen or with the hyphen dropped and the 'mage' part being an identifying description of the referred to person - maybe vocational. As a matter of fact my ‘MSWord’ spell checker (no pun intended) corrects ‘Archmage’ to ‘Arch mage’ two definite and separate words.
I have done a little 'poking around' on the internet today and found that the deeper you dig for an answer, the more interesting the question at hand becomes!
The word 'Arch'
1 on its own and in simple terms means [noun] 'a curved symmetrical structure spanning an opening and typically supporting the weight of a bridge, roof, or wall above it.' or [verb] 'have the curved shape of an arch' or 'form or cause to form the curved shape of an arch'. Used in this sense ‘Arch’ has the origin: Middle English: from Old French
arche, based on Latin
arcus 'bow'.
Quick edit - forgot to mention; sometimes an arch can be seen as being protective and / or supportive af an individual! Just thought I would 'throw that one out there'.In the usage of 'Arch' that is being discussed here though, 'Arch' is used as a prefix to another word and this is where the usage and subsequent pronunciation becomes ... interesting.
Looking at the word ‘Arch’ in the sense of a prefix, it can be seen as being negative or sinister such as in the hyphenated ‘Arch-enemy’
2 or ‘Arch-fiend’. Alternatively, ‘Arch’ can be meant as ‘chief’, ‘over’ or ‘higher’ or ‘of greater rank’ such as in ‘Archbishop’
3 being the chief or higher bishop – in charge of those of lower rank.
There is a suggestion that ‘Archmage’ should be pronounced ‘Ark Mage’ (for example) just as ‘Archangel’ is pronounced ‘Ark Angel’
4. This seems incorrect! In both ‘Archangel’ and ‘Archmage’, the ‘Arch’ part is meant as ‘of higher rank’. It could therefore be argued that the correct pronunciation of ‘Archangel’ should be ‘Arch’ + ‘Angel’ instead of the commonly and seemingly correctly used ‘Ark’ + ‘Angel’ (which I prefer). Time constraints and the fact that this post is already a ‘wall of text’ prohibit me from expanding on the correct or perceived as correct pronunciation of ‘Archangel’ though.
After some consideration, it is my belief that although the word ‘Archmage’ does not seem to exist as a single word in any dictionary it seems that it is valid to use the more common ‘Archmage’ than the seemingly incorrect ‘Arch-mage’ or more correct ‘Arch mage’. It is also my belief that the word ‘Archmage’ should be pronounced ‘Arch’ + ‘mage’ rather than ‘Ark’ + ‘mage’. These are of course only my beliefs and as Forte is reported to have said, “I conceive of nothing, in religion, science or philosophy, that is more than the proper thing to wear, for a while”. Applied to the subject matter in this thread, the Forte quote can easily be pressed into usage for pronunciation!
Enjoy the game everyone and pronounce the words as you see fit.
1. 'Arch' - http://oxforddictionaries.com/definition/arch?q=arch
2. 'Arch-enemy' - http://oxforddictionaries.com/definition/arch-enemy?q=arch-enemy
3. 'Archbishop' - http://oxforddictionaries.com/definition/archbishop?q=archbishop
4. 'Ark Angel' - http://oxforddictionaries.com/definition/archangel?q=archangel ('Ark' or 'Arch' - LOL.)
By the way, great job on the assumptions of what "arch-" means guys. "Overarching," "short for archaic," "just a title," keep it up, maybe we'll get something about foot mages sometime soon XD
My WOT is probably totally incoorect in assumptions, spelling and grandma!

When I read 'foot mages' I thought about fallen arches. (I'm just strange like that!) ROFLmuch.

Edit: Yes! I was bored until reading this thread.